The striker converted a sublime half-volley to put the Gunners ahead in the 19th minute before confidently sliding the ball between Ederson's legs in the second half.
Arsenal kept City at bay in the closing stages to see out the 2-0 victory. The north London club will take on either Manchester United or Chelsea - who face each other on Sunday - in the final on Aug. 1.
Mikel Arteta was positive with his team selection - Aubameyang, Alexandre Lacazette, and Nicolas Pepe were all named in the starting lineup - and that bravery was reflected on the pitch, with Granit Xhaka venturing to just behind the front three when City had the ball in their own defensive third.
City, meanwhile, lacked their usual incisiveness. Raheem Sterling dispossessed Shkodran Mustafi in the Arsenal box in the ninth minute, but he couldn't do anything of worth with the ball. Even Kevin De Bruyne had little joy with his distribution. Things didn't click for City's attack throughout the opening stanza.
Arsenal should've struck in the 16th minute. David Luiz scooped up a poor clearance, and he then hastily threaded a ball through the middle to Aubameyang. The Gunners' top scorer was one-on-one with Ederson, but he wastefully fired straight at the City goalkeeper.
Aubameyang didn't stew on that opportunity and, just a few minutes later, Arsenal were ahead.
Pepe took advantage of the space Benjamin Mendy gave to him, brushing the ball aside so he could hit a left-footed cross. The delivery swerved and looped over Kyle Walker's head before Aubameyang's slick half-volley with the outside of his boot went in off the far post. The Gabonese frontman made an extremely difficult finish look very, very easy.
Ederson had to tip a Mustafi header over the bar minutes before the break, as Arsenal saw out the first period with relative ease. There was work for Pep Guardiola to do at halftime.
City were more purposeful when they again emerged from the guts of Wembley. Soon after blazing one over the bar, Sterling dragged a shot just wide from near the penalty spot following good work from De Bruyne. Emiliano Martinez did well to deny a Riyad Mahrez effort at his near post shortly afterward.
And De Bruyne - his face getting redder and patience thinner - came close when he rippled the side netting with a free-kick in the 61st minute. It seemed like a matter of time before City would draw level.
But Arsenal took their chance when it came. Moments before he was substituted, Pepe did well to fend off Walker while waiting for attacking support to arrive.
The winger played the ball back to Kieran Tierney, and the Scotsman's first-time ball over the top bounced invitingly ahead of Aubameyang. City's backline had no chance of catching up with the Frenchman, who ran through before pushing the ball between Ederson's legs in the 71st minute.
Arsenal then weathered a light storm until the final whistle sounded. Aymeric Laporte's rifled effort from the edge of the area went just wide of the upright in the 83rd minute, but City were still unable to rediscover the penetration that led to 12 goals in their previous three outings.
The Gunners will sign off their Premier League campaign with matches against Aston Villa and Watford before the club competes for its record 14th success in the FA Cup.
"It was a great result against one of the best teams in the world. We were humble, we understood the way we had to play and we took the opportunities to score," Arsenal defender Luiz told BBC Sport after the match.
"We have to be mature, to understand what level we are in the process," he continued. "We have an amazing coach but we can't go from zero to 100. We are improving. The spirit was great and I'm happy for the team because they deserve it."